The present invention relates to a controller using a control algorithm having an IMC (Internal Model Control) structure and, more particularly, to a controller which can perform proper control by automatically correcting the gain of an internal model when the setting of the internal model is improper.
A controller using a control algorithm having an IMC structure has been proposed, which performs control by incorporating an internal model as a mathematical expression of a controlled system process. With this IMC controller, even a controlled system process with a large idle time can be controlled. More specifically, if, for example, the controller is an indoor air conditioner, the controlled system process corresponds to an indoor environment, and the idle time corresponds to the time interval between the instant at which the air conditioner is started and the instant at which the indoor temperature begins to change.
FIG. 1 shows a control system using a conventional IMC controller. Reference numeral 33 denotes a first subtraction processing section for subtracting a feedback amount (to be described later) from a command (set indoor temperature); 32, a filter section for preventing abrupt transfer of a change in output from the first subtraction processing section 33; 34, a manipulating section for calculating a manipulated variable (the temperature of warm or cool air sent from an indoor air conditioner) as an output from this controller on the basis of an output from the filter section 32; 36, an internal model as an approximate mathematical expression of a controlled system process, which model outputs a reference controlled variable corresponding to a controlled variable (indoor temperature) as a control result; 38, a second subtraction processing section for subtracting a reference controlled variable, supplied from the internal model 36, from a controlled variable so as to output a feedback amount; and 40, a controlled system process.
Reference symbols F, Gc, Gm, and Gp denote the transfer functions of the filter section 32, the manipulating section 34, the internal model 36, and the controlled system process 40, respectively; r, a command; u, a manipulated variable; d, a disturbance corresponding to, e.g., an outdoor environment with respect to an indoor environment; y, a controlled variable; ym, a reference controlled variable; and e, a feedback amount.
The operation of this IMC controller will be described next.
First of all, the first subtraction processing section 33 subtracts the feedback amount e from the command r. The result is output to the filter section 32. The manipulating section 34 then calculates the manipulated variable u on the basis of an output from the manipulating section 34. The manipulated variable u is output to the controlled system process 40 and the internal model 36. The second subtraction processing section 38 subtracts the reference controlled variable ym, supplied from the internal model 36 which approximately operates in the same manner as the controlled system process 40, from the controlled variable y of the controlled system process 40. The result is fed back, as the feedback amount e, to the first subtraction processing section 33. In this manner, a feedback control system is formed.
Ideally, the internal model 36 of this IMC controller is mathematically expressed to be perfectly identical to the controlled system process 40. It is also ideal that the manipulating section 34 has an inverse characteristic (1/Gm) of the transfer function of the internal model 36. However, it is impossible to obtain the reciprocal of a factor associated with the idle time of the internal model 36. For this reason, the factor associated with the idle time is generally neglected.
With such an arrangement, therefore, the controlled variable y can be obtained from the command r and the disturbance d according to the following equation: ##EQU1##
Assume that the transfer function Gm of the internal model 36 is equal to the transfer function Gp of the controlled system process 40, and the transfer function Gc of the manipulating section 34 is equal to the reciprocal (1/Gm=1/Gp) of the transfer function of the internal model 36. In this ideal state, equation (1) can be rewritten into EQU y=F.times.r+(1-F).times.d (2)
Also assume that there is no abrupt change in the command r. Under such an ideal condition, the filter section 32 can be omitted, and F=1 can be set. Therefore, the controlled variable y becomes equal to the command r (y=r) to realize control without any influence of the disturbance d.
Consider the disturbance d next. Even if both the controlled system process 40 and the internal model 36 have a long idle time, they exhibit the same characteristics with respect to the manipulated variable u. Consequently, the feedback amount e output from the second subtraction processing section 38 is only the disturbance d. It is, therefore, apparent that the disturbance d can be controlled.
Such an IMC controller is generally designed on the basis of design conditions associated with robust stability and robust performance respectively indicating stability and performance obtained when the model identification error between the controlled system process 40 and the internal model 36 becomes large.
When the internal model 36 is determined by such a model identification technique, some model identification error in the internal model 36 relative to the controlled system process 40 cannot be avoided. If, however, this model identification error is erroneously estimated, control cannot be performed as expected. Countermeasures against this situation are taken by an expert in control.
A conventional IMC controller is arranged in the above-described manner. In a controller having a internal model which is greatly different from a controlled system process, when a change in command, a disturbance, changes in the characteristics of the controlled system process, or the like, which shifts control to a transient state, occurs, fluctuations in controlled variable occur. As a result, instability of this control cannot be suppressed. In this case, an operator other than an expert in control must give up the use of the IMC controller.
This problem will be described below with reference to FIG. 2. Assume that a conventional IMC controller (Internal Model Controller) is used to perform temperature control of an industrial electric furnace. In the case shown in FIG. 2, the controlled variable y is the temperature in the furnace, and the manipulated variable u is an output from a heater. The controller is used to adjust the temperature in the furnace to a command. The command is input, as the desired value r, to the controller. In general, the command r, the controlled variable y, and the manipulated variable u in the controller are expressed as values normalized within the range of 0% to 100%. A change in a designated value from the controller in response to an output, as a manipulated variable, from the heater is transferred to the temperature, as a controlled variable, in the furnace. This transfer characteristic can be defined as the transfer function Gp. The simplest expression of this transfer function is 1st-order delay+idle time and given by EQU Gp=Kexp(-Ls)/(1+Ts)
where K is the process gain, L is the idle time, and T is the process time constant. This equation indicates the following characteristics. When the designated value from the controller changes by 1% in response to an output from the heater, the temperature in the furnace changes by K%. The time interval between the instant at which the designated value from the controller changes by, e.g., 1% in response to an output from the controller and the instant at which the temperature in the furnace substantially begins to change is the process idle time L. The time interval between the instant at which the temperature in the furnace begins to change (after the lapse of the process idle time L since the designated value from the controller has changed by, e.g., 1% in response to an output from the heater) and the instant at which the temperature in the furnace changes by 0.63 K% is the process time constant T.
In the electric furnace, since it takes much time for an output from the heater itself to change, the process idle time is close to the process time constant in the characteristics of the transfer function. In general, such a value is large as a process idle time. It is difficult to apply PID control, which has been most widely used, to a controlled system having such characteristics. An IMC, however, is an effective means for this controlled system.
The purpose of control is to keep the temperature in the furnace constant. The internal model parameters of the IMC controller are generally adjusted by the designer/manufacturer of the electric furnace or a field operator. The designer/manufacturer of the electric furnace tends to lack in knowledge of control. Even if the designer/manufacturer has knowledge of control, he/she cannot properly adjust the parameters because he/she does not perform adjustment during an operation of the electric furnace. On the other hand, the field operator generally performs adjustment by a trial-and-error method which is not based on knowledge of control. Therefore, it takes much time and labor to realize proper adjustment. For these reasons, a conventional IMC controller is often used without proper adjustment.
In addition, the number of products transferred through the electric furnace during an operation of the furnace often and irregularly varies. Furthermore, the number of types of products transferred through the furnace is not limited to one. If the furnace is an electric furnace for precision machine components, the type of products transferred through the furnace may change every several hours. Such a change in type becomes a factor of variations in the characteristics of the controlled system process. The electric furnace itself is affected by the indoor temperature of the factory or other heating elements, which become factors of variations in characteristics. In this case, even if the internal model parameters of the IMC controller are properly adjusted in the process of installing the electric furnace, proper control cannot be maintained.
Assume that the type of products transferred through the electric furnace changes. In this case, the temperature (command) to be maintained in the furnace also changes. As the command changes, control is shifted from a settled state to a transient state. At this time, with the above improper adjustment and variations in the characteristics of the controlled system process, control lacks stability, resulting in fluctuations in temperature in the furnace, or control becomes excessively stable, excessively prolonging the time required for the temperature in the furnace to reach a command. These phenomena lead to a deterioration in the productivity of the electric furnace or generation of defective products.
In general, variations in the characteristics of an electric furnace are caused by the improper setting of the internal model parameters of an IMC, especially a model gain. If such variations in characteristics occur frequently and irregularly, it is difficult for a field operator to adjust even the model gain. Therefore, practical use of an IMC is difficult to realize unless the model gain is automatically adjusted in accordance with a situation. Consequently, practical use of such an electric furnace must be abandoned.